Mathematical Modeling of the Molecular Weight Distribution in Low Density Polyethylene. I. Steady‐State Operation of Multizone Autoclave Reactors

López‐Carpy, Bruno; Saldívar‐Guerra, Enrique; Zapata‐González, Iván; García-Franco, César A.

doi:10.1002/mren.201800013

Cited by 9 publications

(3 citation statements)

References 54 publications

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“…If many LCBs are formed, binary trees from the previous section are not really user-friendly because the length of an LCB can be quite high (in the limit, similar to the backbone length), and thus large composite trees would be needed. A key example is highly branched low-density polyethylene (LDPE) for which it is desired to keep a record of the LCB length and its position onto the backbone for property control. ,− …”

Section: Tree- and Matrix-based Data Structures To Represent Distribu...mentioning

confidence: 99%

Gillespie-Driven kinetic Monte Carlo Algorithms to Model Events for Bulk or Solution (Bio)Chemical Systems Containing Elemental and Distributed Species

Trigilio

Marien

Steenberge

et al. 2020

Ind. Eng. Chem. Res.

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Stochastic modeling techniques have emerged as a powerful tool to study the time evolution of processes in many research fields including (bio)chemical engineering and biology. One of the most applied techniques is kinetic Monte Carlo (kMC) modeling according to the stochastic simulation algorithm (SSA) as pioneered by Gillespie, in which MC channels and time steps are discretely sampled from probability distributions. In the last decades, the SSA algorithm, as originally developed for systems with elemental species (e.g., A, B, C, etc.), has been further adapted (i) to also tackle systems with distributed species, therefore, populations and (ii) to enable faster algorithm execution. In the present contribution, we highlight the most important developments, taking bulk/solution polymerization as the reference distributed chemical process. We address SSA principles based on conventional array data structures, common acceleration methods (e.g., τ leaping and the scaling method), and the strength of tree- and matrix-based data structures for detailed storage of molecular information per distribution type and even individual population member. In addition, we report advancement regarding array programming and MC sampling methods complemented by the introduction of the use of higher-order trees and root-finding sampling tools. The contribution gives thus a detailed overview of the available main kMC algorithm steps to study kinetics, irrespective of the specific field of application due to their generic nature.

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Section: Tree- and Matrix-based Data Structures To Represent Distribu...mentioning

confidence: 99%

Gillespie-Driven kinetic Monte Carlo Algorithms to Model Events for Bulk or Solution (Bio)Chemical Systems Containing Elemental and Distributed Species

Trigilio

Marien

Steenberge

et al. 2020

Ind. Eng. Chem. Res.

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show abstract

“…The moments of the radicals and dead polymers can be expressed by applying the moment equation. Because the concentration and decomposition rate of the initiator are negligible compared to those of the other monomers and dead polymer and because each zone acts like the CSTR in the stationary state, the quasi-steady-state approximation can be applied to the 0th, 1st, and 2nd moments of the radicals and the reaction rates for the 0th, 1st, 2nd, and 3rd moments of the dead polymers, ,, as shown in Table .…”

Section: Methodsmentioning

confidence: 99%

“…For this reason, theoretical models of the polymerization process have been developed to allow the prediction of polymer properties under given operating conditions. For example, the kinetic mechanism of free-radical polymerization has been proposed in earlier studies, and the method of moments has been used for the calculation of molecular weight averages. − In addition, the polymerization kinetic model represented by moments has been combined with a multizone reactor model in which each zone is considered to be a well-mixed continuous stirred-tank reactor (CSTR) for the calculation of the temperature distribution from top to bottom of the reactor. − However, in these studies, the zones were directly arranged from the inlet to the outlet because the flow pattern was unknown; thus, the back-mixing flow rate from the lower to the upper zones was determined by the user. However, the flow pattern induced by the stirrer can be efficiently solved and analyzed using computational fluid dynamics (CFD), and there are several previous examples of the simulation of low-density polyethylene production in a high-pressure autoclave reactor using CFD models.…”

Section: Introductionmentioning

confidence: 99%

Multicompartment Model of an Ethylene–Vinyl Acetate Autoclave Reactor: A Combined Computational Fluid Dynamics and Polymerization Kinetics Model

Lee

Jeon

Cho

et al. 2019

Ind. Eng. Chem. Res.

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In this paper, we present a multicompartment model of an ethylene–vinyl acetate autoclave reactor including the mixing effects of the stirring device analyzed using computational fluid dynamics; the model is simplified by cell aggregation, and the polymerization kinetics is modeled with the method of moments. The proposed model has been verified through comparison of the predicted product properties and locally distributed temperatures with those from an industrial plant. The proposed model, which is capable of simulating a complex system with low computational load, can be applied to maintain consistent product quality, prevent undesired thermal runaway, and optimize the conversion and production rates.

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Polymer Reaction Engineering

Saldívar‐Guerra¹

2019

Encyclopedia of Polymer Science and Technology

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Polymer reaction engineering is a discipline that encompasses a set of principles and tools for the scaling up, design, analysis, control, troubleshooting, and optimization of industrial polymerization processes. Its tools are widely used in industry and are mainly taken from the fields of reaction kinetics, chemical reactor engineering, thermodynamics, physical chemistry, and applied mathematics. In this article, the basics to go from the polymerization reaction kinetics to reactor modeling are first introduced. Then, molecular weight distribution (MWDs) modeling tools are reviewed; these are classified and discussed as: analytical techniques, the method of moments, and numerical techniques for the complete MWD, covering both deterministic and stochastic methods. Next, the theoretical bases of copolymerization systems are discussed, including copolymerization models for copolymer composition and reactivity ratio estimation, to conclude with the discussion of the pseudo‐homopolymerization approach (or apparent rate constants method) for the modeling of the MWD in copolymerization systems. A section providing a general description of heterogeneous processes and their modeling is also included, covering the topics of population balance equations, suspension polymerization and emulsion polymerization. The article ends with a brief discussion of future perspectives in the field.

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Mathematical Modeling of the Molecular Weight Distribution in Low Density Polyethylene. I. Steady‐State Operation of Multizone Autoclave Reactors

Cited by 9 publications

References 54 publications

Gillespie-Driven kinetic Monte Carlo Algorithms to Model Events for Bulk or Solution (Bio)Chemical Systems Containing Elemental and Distributed Species

Gillespie-Driven kinetic Monte Carlo Algorithms to Model Events for Bulk or Solution (Bio)Chemical Systems Containing Elemental and Distributed Species

Multicompartment Model of an Ethylene–Vinyl Acetate Autoclave Reactor: A Combined Computational Fluid Dynamics and Polymerization Kinetics Model

Polymer Reaction Engineering

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